1) The radius of hemispherical balloon increase from 7 cm to 14 cm as air is being pumped into it. Find the ratios of the surface areas of the balloon in two cases. Solution :
For 1st hemisphere,
r = 7 cm
TSA -1 = 3 π r2
⇒ = 3 x π x 72

TSA-1 3 π x 72 1-------- = --------- = ---- TSA -2 3π x 142 4

⇒ S1 : S2 = 1 : 4
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2) Show that the surface area of sphere is same as that of the lateral surface area of a cylinder that just encloses the sphere.Solution :
Total surface area of sphere = 4 π r2 ------(1)
The radius and height of the cylinder that just encloses the sphere of radius r and 2r respectively.
∴ CSA of cylinder = 2 π r h
⇒ = 2 π r x 2r
∴ CSA of cylinder = 4 π r2 ----(2)
∴ From (1) and (2)
Surface area of sphere is same as that of the lateral surface area of a cylinder that just encloses the sphere.Surface Area :